Infantino wrote to all 211 Fifa member associations, saying each would receive $40m (£30m) if they supported his contentious proposal, and set a 19 September deadline to access an initial $20m (£15m).
Thrive Eternal was expected to head the proposed investor consortium for FFE.
Thrive is a US venture capital firm founded by Joshua Kushner, the brother of Jared Kushner, son-in-law to former US President Donald Trump.
Uefa demanded all materials related to the investment plan, including emails, instant messages (WhatsApp, Signal, Teams, Slack or other platforms), SMS, written correspondence and meeting notes, as well as any communications involving Fifa officials, staff, committee members, consultants or agents, and any Fifa member association, confederation, broadcaster, sponsor or financial institution.
Regarding the 19 September deadline, Uefa also sought preservation of documents about the payment structure for Fifa member associations, including its design, modelling, legal basis, approvals and communications to members.
Uefa asked Infantino to confirm in writing within five business days that he had received and understood the notice and had taken immediate steps to preserve the relevant materials.
Uefa vice-president Laura McAllister called the potential legal action a clear call to address what she described as an abysmal governance process leading up to the FFE initiative.
Speaking to BBC Radio 5 Live, she said the sport must learn from a disastrous process and ensure proper accountability to prevent a repeat.
She hopes others will withdraw their backing for Infantino, calling this a pivotal moment in football’s history.
“We cannot keep putting out fires because of unilateral plans,” McAllister said, adding: “I really hope now that we can have a change of leadership next year.”
As pressure mounts on Infantino with Serbia, Sweden and Finland pulling their support, Qatar, Lebanon, Kuwait and Sri Lanka have pledged to back his continued leadership of Fifa.
Uefa holds 55 votes, Africa 54, Asia 46, Concacaf 35, Oceania 11 and Conmebol 10.
The Asian Football Confederation (AFC) said it stands in solidarity with Uefa and Concacaf, while Africa, Conmebol and Oceania have not criticised Infantino’s plan.
However, the Fifa Council could seek to force Infantino’s resignation via an emergency meeting, which would be triggered if 19 of the 37 council members request one, and must be held within two weeks.
The council includes nine members from Uefa, seven from the AFC, five from Concacaf, six from Africa, five from Conmebol and three from Oceania, along with Infantino and secretary general Mattias Grafstrom.